Beliefs, Models, Analogies

Theory of Levels of Langauge and the Theory of Logical Types

"Perhaps the most famous of all semantical antimonies is that of the
man who says of himself, I am lying.' On following this statement to its logical conclusion, we
find again that it is true only if it is not true; in other words, the man is lying only if he is telling
the truth, and vice-versa, truthful when he is lying. In this case, the theory of logical types cannot
be used to eliminate the antimony, for words or combinations of words do not have a logico-type
hierarchy. To the best of our knowledge, it was again Bertrand Rusself who first though of a
solution. In the last paragraph of his introduction of Wittgenstein's Tracticus Logico-Philosophicus he suggests in an almost indentical fashion, that every language has, as
Mr. Wittegenstein says, a structure concerning which, in the language, nothing can be said, but
that there may be another language dealing with the structure, and that to this hierarchy, of
languages, there may be no limit'. This suggestion was developed, mainly be Carnap and by
Tarski, into what is now known as the theory of levels of language. In analogy to the
theory of logical types, this theory safeguards against the confusion of levels."